[math-fun] Backwards Bekenstein argument?
Bekenstein found that the entropy of a black hole was proportional to its surface area, which is also related to its mass. Since Newton, we've always assumed that mass is the "source" of gravity, but perhaps we (and Newton) were misled in the pre-digital world. Perhaps gravity (and particularly the space-time curvature) is really "caused" by the information stored on the Bekenstein surface, and the numerical value of the mass (& hence energy) is merely some statistic associated with this information. Verlinde's ideas of a few years ago are in this direction; I'm not sure where his thinking has led him recently.
But then what is the source of Earth's gravity? -- Gene
________________________________ From: Henry Baker <hbaker1@pipeline.com> To: math-fun@mailman.xmission.com Sent: Friday, July 25, 2014 10:31 AM Subject: [math-fun] Backwards Bekenstein argument?
Bekenstein found that the entropy of a black hole was proportional to its surface area, which is also related to its mass.
Since Newton, we've always assumed that mass is the "source" of gravity, but perhaps we (and Newton) were misled in the pre-digital world.
Perhaps gravity (and particularly the space-time curvature) is really "caused" by the information stored on the Bekenstein surface, and the numerical value of the mass (& hence energy) is merely some statistic associated with this information.
Verlinde's ideas of a few years ago are in this direction; I'm not sure where his thinking has led him recently.
On 7/25/2014 10:31 AM, Henry Baker wrote:
Bekenstein found that the entropy of a black hole was proportional to its surface area, which is also related to its mass.
Since Newton, we've always assumed that mass is the "source" of gravity, but perhaps we (and Newton) were misled in the pre-digital world.
In general relativity Einstein's equations have source-free solutions, e.g. gravity waves, de Sitter space.
Perhaps gravity (and particularly the space-time curvature) is really "caused" by the information stored on the Bekenstein surface, and the numerical value of the mass (& hence energy) is merely some statistic associated with this information.
Verlinde's ideas of a few years ago are in this direction; I'm not sure where his thinking has led him recently.
Padmanabhan actually preceded Verlinde and has done more with the idea. http://arxiv.org/pdf/0911.5004.pdf Sakharov originated the idea of gravity as a kind of statistical force. Here's review by Visser http://arxiv.org/abs/grqc/0204062 Brent Meeker
(Especially to Neil): Can anyone offer a pointer to writings about good [lattices, sphere-packings, or kissing configurations] in Hilbert space?* Thanks, Dan __________________________________________________________ * Specifically, square-summable sequences of real numbers.
Suppose we roll a unit-radius ball without slipping along a closed curve C on the xy-plane in 3-space. This will have the net effect of applying some rotation to the ball. For instance, if C is an equilateral triangle of side-length = π, the net rotation will switch the N and S poles of the ball. QUESTION: What is the shortest closed curve C shorter than 3π that also switches the ball's poles? (Or at least, what is the inf of the lengths of all closed curves C that switch the poles?) --Dan
Spinning the ball about the vertical (z) axis, and not having it move in the xy-plane, is technically “rolling without slipping”. So unless you modify your question, the length of the shortest C is zero, if I’m allowed to put N and S where I choose, or pi, if N and S start on a vertical axis. -Veit On Jul 28, 2014, at 11:26 AM, Dan Asimov <dasimov@earthlink.net> wrote:
Suppose we roll a unit-radius ball without slipping along a closed curve C on the xy-plane in 3-space.
This will have the net effect of applying some rotation to the ball.
For instance, if C is an equilateral triangle of side-length = π, the net rotation will switch the N and S poles of the ball.
QUESTION: What is the shortest closed curve C shorter than 3π that also switches the ball's poles? (Or at least, what is the inf of the lengths of all closed curves C that switch the poles?)
--Dan
Right: spinning is not permitted. (Though I wouldn't have called it "rolling".) --Dan On Jul 29, 2014, at 7:21 AM, Veit Elser <ve10@cornell.edu> wrote:
Spinning the ball about the vertical (z) axis, and not having it move in the xy-plane, is technically “rolling without slipping”. So unless you modify your question, the length of the shortest C is zero, if I’m allowed to put N and S where I choose, or pi, if N and S start on a vertical axis.
participants (5)
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Dan Asimov -
Eugene Salamin -
Henry Baker -
meekerdb -
Veit Elser